Bessel
cern.jet.math

Class Bessel



  • public class Besselextends Constants
    Bessel and Airy functions.
    • Method Summary

      Methods 
      Modifier and TypeMethod and Description
      static doublei0(double x)
      Returns the modified Bessel function of order 0 of the argument.
      static doublei0e(double x)
      Returns the exponentially scaled modified Bessel function of order 0 of the argument.
      static doublei1(double x)
      Returns the modified Bessel function of order 1 of the argument.
      static doublei1e(double x)
      Returns the exponentially scaled modified Bessel function of order 1 of the argument.
      static doublej0(double x)
      Returns the Bessel function of the first kind of order 0 of the argument.
      static doublej1(double x)
      Returns the Bessel function of the first kind of order 1 of the argument.
      static doublejn(int n, double x)
      Returns the Bessel function of the first kind of order n of the argument.
      static doublek0(double x)
      Returns the modified Bessel function of the third kind of order 0 of the argument.
      static doublek0e(double x)
      Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
      static doublek1(double x)
      Returns the modified Bessel function of the third kind of order 1 of the argument.
      static doublek1e(double x)
      Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.
      static doublekn(int nn, double x)
      Returns the modified Bessel function of the third kind of order nn of the argument.
      static doubley0(double x)
      Returns the Bessel function of the second kind of order 0 of the argument.
      static doubley1(double x)
      Returns the Bessel function of the second kind of order 1 of the argument.
      static doubleyn(int n, double x)
      Returns the Bessel function of the second kind of order n of the argument.
    • Method Detail

      • i0

        public static double i0(double x)                 throws ArithmeticException
        Returns the modified Bessel function of order 0 of the argument.

        The function is defined as i0(x) = j0( ix ).

        The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • i0e

        public static double i0e(double x)                  throws ArithmeticException
        Returns the exponentially scaled modified Bessel function of order 0 of the argument.

        The function is defined as i0e(x) = exp(-|x|) j0( ix ).

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • i1

        public static double i1(double x)                 throws ArithmeticException
        Returns the modified Bessel function of order 1 of the argument.

        The function is defined as i1(x) = -i j1( ix ).

        The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • i1e

        public static double i1e(double x)                  throws ArithmeticException
        Returns the exponentially scaled modified Bessel function of order 1 of the argument.

        The function is defined as i1(x) = -i exp(-|x|) j1( ix ).

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • j0

        public static double j0(double x)                 throws ArithmeticException
        Returns the Bessel function of the first kind of order 0 of the argument.
        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • j1

        public static double j1(double x)                 throws ArithmeticException
        Returns the Bessel function of the first kind of order 1 of the argument.
        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • jn

        public static double jn(int n,        double x)                 throws ArithmeticException
        Returns the Bessel function of the first kind of order n of the argument.
        Parameters:
        n - the order of the Bessel function.
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • k0

        public static double k0(double x)                 throws ArithmeticException
        Returns the modified Bessel function of the third kind of order 0 of the argument.

        The range is partitioned into the two intervals [0,8] and (8, infinity). Chebyshev polynomial expansions are employed in each interval.

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • k0e

        public static double k0e(double x)                  throws ArithmeticException
        Returns the exponentially scaled modified Bessel function of the third kind of order 0 of the argument.
        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • k1

        public static double k1(double x)                 throws ArithmeticException
        Returns the modified Bessel function of the third kind of order 1 of the argument.

        The range is partitioned into the two intervals [0,2] and (2, infinity). Chebyshev polynomial expansions are employed in each interval.

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • k1e

        public static double k1e(double x)                  throws ArithmeticException
        Returns the exponentially scaled modified Bessel function of the third kind of order 1 of the argument.

        k1e(x) = exp(x) * k1(x).

        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • kn

        public static double kn(int nn,        double x)                 throws ArithmeticException
        Returns the modified Bessel function of the third kind of order nn of the argument.

        The range is partitioned into the two intervals [0,9.55] and (9.55, infinity). An ascending power series is used in the low range, and an asymptotic expansion in the high range.

        Parameters:
        nn - the order of the Bessel function.
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • y0

        public static double y0(double x)                 throws ArithmeticException
        Returns the Bessel function of the second kind of order 0 of the argument.
        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • y1

        public static double y1(double x)                 throws ArithmeticException
        Returns the Bessel function of the second kind of order 1 of the argument.
        Parameters:
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException
      • yn

        public static double yn(int n,        double x)                 throws ArithmeticException
        Returns the Bessel function of the second kind of order n of the argument.
        Parameters:
        n - the order of the Bessel function.
        x - the value to compute the bessel function of.
        Throws:
        ArithmeticException

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